Question

What is the quotient of the following 24x to the 6 - 30X to the 4th divided by 6X squared

Answer 1

To find the quotient of \( 24x^6 - 30x^4 \) divided by \( 6x^2 \), we can follow these steps:

1. Factor out the common term from the numerator.
2. Divide each term in the numerator by \( 6x^2 \).

Let's start with the expression:

\[
\frac{24x^6 - 30x^4}{6x^2}
\]

### Step 1: Factor out the common term from the numerator.
We can factor out \( 6x^4 \) from the numerator:

\[
24x^6 - 30x^4 = 6x^4(4x^2 - 5)
\]

### Step 2: Substitute the factored form back into the quotient.
Now substitute the factored form into the division:

\[
\frac{6x^4(4x^2 - 5)}{6x^2}
\]

### Step 3: Simplify the expression.
We can now cancel \( 6 \) from the numerator and the denominator, and also \( x^2 \):

\[
\frac{x^4(4x^2 - 5)}{x^2} = x^{4-2}(4x^2 - 5) = x^2(4x^2 - 5)
\]

### Final Result:
The quotient is:

\[
x^2(4x^2 - 5)
\]

This can also be expressed as:

\[
4x^4 - 5x^2
\]

Either form is acceptable, but the expression \( x^2(4x^2 - 5) \) is a simpler factored form.